A- and B-stability for Runge-Kutta methods-characterizations and equivalence

Using a special representation of Runge-Kutta methods (W-transformation), simple characterizations of A-stability and B-stability have been obtained in [9, 8, 7]. In this article we will make this representation and their conclusions more transparent by considering the "exact Runge-Kutta method". Finally we demonstrate by a numerical example that for difficult problems B-stable methods are superior to methods which are only A-stable.